The product of the polynomials (4 + 2x³)(4 − 2x³) is 16 - 4x⁶
How to determine the product of the polynomialsFrom the question, we have the following parameters that can be used in our computation:
Polynomial products: (4 + 2x3 )(4 − 2x3 )
Rewrite the above product properly
So, we have the following representation
Polynomial products = (4 + 2x³)(4 − 2x³)
Using the difference of two squares identity
We have the following representation
Polynomial products = (4)² - (2x³)²
Evaluate the exponents
Polynomial products = 16 - 4x⁶
Hence, the product is 16 - 4x⁶
Read more about polynomials at
https://brainly.com/question/17517586
#SPJ1
The length of the longer leg of a right triangle is 6inches more than twice the length of the shorter leg. The length of the hypotenuse is 9inches more than twice the length of the shorter leg. Find the side lengths of the triangle.
The length of shorter leg is 15 inches, length of longer leg is 36 inches and the length of hypotenuse is 39 inches.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.
Let,
x = Longer leg of triangle
y = Shorter leg of triangle
h = Hypotenuse of triangle
Given: The length of the longer leg of a right triangle is 6inches more than twice the length of the shorter leg.
The length of the hypotenuse is 9inches more than twice the length of the shorter leg.
⇒ x = 6 + 2y
h = 9 + 2y
The given triangle is a right angled triangle.
⇒ x^2 + y^2 = h^2
(6 + 2y)^2 + y^2 = (9 + 2y)^2
36 + 24y + 4y^2 + y^2 = 81 + 36y + 4y^2
36 + 24y + 5y^2 = 81 + 36y + 4y^2
36 - 81 + 24y - 36y + 5y^2 - 4y^2 = 0
-45 - 12y + y^2 = 0
y^2 - 12y - 45 = 0
y^2 - 15y + 3y - 45 = 0
y(y - 15) + 3(y - 15) = 0
(y - 15)(y + 3) = 0
y - 15 = 0, y + 3 = 0
y = 15, y = -3
Since the length is not negative.
So, y = 15
Hence,
Shorter leg = 15 inchs
Longer leg = 6 + 2y = 6 + 2(15) = 36 inches
Hypotenuse = 9 + 2y = 9 + 2(15) = 39 inches
To know more about right triangle, click on the link
https://brainly.com/question/2437195
#SPJ1
when asked to rewrite 27+45 as a product of the GCF and a sum of two numbers, a student wrote 3(9+15). is the student correct? why or why not?
Answer:correct
Step-by-step explanation: If you distribute the 3 to 9 and 15 you will get this,
3x9 + 15x3
27 + 45
Rewrite 302+40=342 in a different way, using the commutative of addition
Answer:
40+32=342
Step-by-step explanation:
Using the commutative of addition change the position of 302 and 40 the expression is 40+302=342 [analysis]
Let f(x) = 5(3)x
The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x).
Choose the equation of g(x).
Responses
g(x) = 10(3)xg(x) = 10(3)x
g(x) = 7(3)xg(x) = 7(3)x
g(x) = 2(3)xg(x) = 2(3)x
g(x) = 5(6)x
The required equation is g(x) = 10(3)x which is the correct answer would be an option (A).
The graph of g(x) is obtained by stretching the graph of f(x) vertically by a factor of 2.
Since the vertical stretch of a graph multiplies the y-coordinates of each point on the graph by a constant factor, the equation of g(x) must be obtained by multiplying the y-coordinate of each point on the graph of f(x) by 2.
In the given equation f(x) = 5(3)x, the y-coordinate of each point on the graph of f(x) is 5(3)x.
Thus, to stretch the graph of f(x) vertically by a factor of 2, we need to multiply this y-coordinate by 2 to get the y-coordinate of the corresponding point on the graph of g(x). This gives us the following equation for g(x):
⇒ g(x) = 2 × 5(3)x = 10(3)x
Therefore, the required equation is g(x) = 10(3)x.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ1
Please help, this is on final. I need how you got the answer and what the answer is.
Answer:
Angle 1 is congruent to the angle that is supplementary to angle 2. Angle 2 is also congruent to angle 3 due to the Corresponding angles theorem. Since angle 2 is supplementary to angle 1 and angle 3 is congruent to angle 2. This shows that angle 1 and angle 3 are supplementary.
Step-by-step explanation:
Answer:
I can't see it that wel..?m
Are the triangles similaeu, if so write how you know
Answer:
Triangles BAD and CED have angle D in common.
<D is congruent to itself, so <D of triangle BAD is congruent to <D of triangle CED. That is 1 pair of congruent angles.
<A is a right angle. <CED is a right angle.
Theorem: All right angles are congruent.
<A is congruent to <CED. That is a second pair of congruent angles.
By AA Similarity, triangles BAD and CED are similar.
What is the value of 2cos2(105⁰) − 1? Negative StartFraction StartRoot 3 EndRoot Over 2 EndFraction Negative one-half One-half StartFraction StartRoot 3 EndRoot Over 2 EndFraction
Answer: - sqrt3/2
Step-by-step explanation:
Which of the following is a solution to the inequality below? –5 ≥ –1 + s
The solution of the inequality –5 ≥ –1 + s will be less than or equal to negative 4.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
–5 ≥ –1 + s
Simplify the inequality, then the value of the variable 's' is given as,
–5 ≥ –1 + s
–5 + 1 ≥ s
s ≤ –4
The solution of the inequality –5 ≥ –1 + s will be less than or equal to negative 4.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ1
RHOM is a rhombus with point O at the origin. Find the
x-coordinate
of point M.
01
02
03
04
M (7,4)
R
H (5,0)
The points on the rhombus M(?, 0) and H(5, 0), and the location of the point O of the rhombus, indicates that the length of a side of a rhombus is 5 units from which Pythagorean Theorem indicates that the x-coordinate of the point M is 3
What does the Pythagorean Theorem state?Pythagorean Theorem states that the sum of the squares of the legs of a right triangle is equivalent to the square of the length of the hypotenuse side of a right triangle.
The shape of the quadrilateral RHOM = A rhombus
The specified coordinates of the vertices of the rhombus are;
Point M = (?, 4)
Point H = (5, 0)
A rhombus is a parallelogram that have all four sides of the same length
The length of side OH, which is on the x-axis = 5 - 0 = 5
Therefore, the length of OM = 5 (properties of a rhombus)
Let x represent the x-coordinate of the point M
According to Pythagorean Theorem, we get;
x² + 4² = 5²
Where x = The horizontal distance of the point M from the y-axis
x² = 5² - 4² = 9
x = √9 = 3
The x-coordinate of the point M, x = 3
Learn more about a rhombus here:
https://brainly.com/question/23432950
#SPJ1
A ball is drawn randomly from a jar that contains 5 red balls, 2 white balls, and 1 yellow ball. Find the probability of: Find P(red ball): Find P(NOT Yellow): Find P(white or yellow)
The answers to all the subparts using the probability formula are shown:
(A) P(red ball): 5/8
(B) P(NOT Yellow): 7/8
(C) P(white or yellow): 3/8
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
PRobability formula: P(E) = favourable events/Total events
(A) P(red ball):
P(E) = favorable events/Total events
P(E) = 5/8
(B) P(NOT Yellow)
P(E) = favorable events/Total events
P(E) = 7/8
(C) P(white or yellow)
P(E) = favorable events/Total events
P(E) = 3/8
Therefore, the answers to all the subparts using the probability formula are shown:
(A) P(red ball): 5/8
(B) P(NOT Yellow): 7/8
(C) P(white or yellow): 3/8
Know more about probability here:
https://brainly.com/question/28924396
#SPJ1
is 1+1=11 or does 1+1= window
Answer:
Step-by-step explanation:
Probably "1+1=window" was discovered by some cheeky primary school student, and then it spread without attribution. We will never know for sure who originally came up with that.
A store is selling an NBA jersey for $60 that has been discounted by 25%. What is the original selling price?
The original selling price is $80 if A store is selling an NBA jersey for $60 that has been discounted by 25%.
Define discount.The difference between the purchase price and the item's par value is the discount. Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
Given,
Discount = 25%
Selling price = $60
Original price = x
Original price
= Selling price/1 - discount
= 60/ 1 - 0.25
= 60/ 0.75
= 80
The original selling price is $80 if A store is selling an NBA jersey for $60 that has been discounted by 25%.
To learn more about discount, visit:
https://brainly.com/question/29205061
#SPJ1
Mrs. Feinman has 20 boxes of markers. Next year, She plans to buy 560% more boxes. How many boxes will she have in all? Group of answer choices
Answer:
112
Step-by-step explanation:
Find the area between the curves y=x^2 and y=-3*x
the area between the curves y=[tex]x^{2}[/tex] and y=-3x is 9/2 sq units
What is the area of the curve?By performing a definite integral between the two point, one may determine the area under a curve between two points. Integrate y = f(x) between the limits of a and b to determine the area under the curve y = f(x) between x = a & x = b. With the specified restrictions, integration may be used to compute this area.
The area between the curves y=[tex]x^{2}[/tex] and y=-3x
y=[tex]x^{2}[/tex] and y=-3x
firstly calculated the point of intersection. y = y
[tex]x^{2}[/tex] = -3x
[tex]x^{2}[/tex] + 3x = 0
x( x+ 3) = 0
x = 0 , x = -3
point of intersection is 0 , -3
Area = [tex]\int\limits _ {} \, x^{2} + 3xdx[/tex] from -3 to 0
Area = [ [tex]x^{3}/3 + 3x^{2} /2[/tex] ] from -3 to 0
Area = [ -27/3 + 27/2 ]
Area = [ -9 + 27/2]
Area = [-18 + 27] / 2
Area = 9/2 sq units
To know more about area of curve click the link:
brainly.com/question/9296915
#SPJ1
Use the quadratic formula to find the solutions to the quadratic equation
below.
2x²-5x+ 5 = 0
O A. x=-
OB. X=
O C. x=
5±i√55
4
OD. X=-
5± √15
4
5± √55
4
5+√15
4
A quadratic equation's solutions can be found using the quadratic formula, which is option D.
What's the quadratic equation's formula?Any quadratic problem can be resolved using the quadratic formula. First, we change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. Then, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). View examples of how to apply the formula to a range of equations.If necessary, simplify the right side while writing the left side as a square. Create two linear equations by combining the positive and negative square roots of the right side with the square root of the left side. Each of the two linear equations must be resolved.Explanation:
2x^2 - 5x +5 = 0.
x = - 5 +-[tex]\sqrt{5[/tex].
To learn more about Quadratic equation's refer to:
https://brainly.com/question/1214333
#SPJ1
A quadratic equation's solutions can be found using the quadratic formula, which is option D.
What's the quadratic equation's formula?Any quadratic problem can be resolved using the quadratic formula. First, we change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. Then, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). View examples of how to apply the formula to a range of equations.
If necessary, simplify the right side while writing the left side as a square. Create two linear equations by combining the positive and negative square roots of the right side with the square root of the left side. Each of the two linear equations must be resolved.
2x^2 - 5x +5 = 0.
x = - 5 [tex]\pm[/tex] √5
To learn more about Quadratic equation's refer to:
brainly.com/question/1214333
#SPJ1
Marissa's mom purchased coffee from the local coffee shop. The first cup of coffee was $2.95. Each refill is $1.50. She also decided to get a bagel for $2.75. If Marissa's mom had 2 refills and a $0.50 discount as part of the rewards program, how much did she spend at the coffee shop?
$7.20
$7.45
$8.20
$9.45
By evaluating a linear equation, we get that the amount she spent is $ 8.20 at the coffee shop.
What is linear equation explain?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept is called a "linear equation of two variables," where y and x are the variables.
Assuming x refills, the price is $ 2.95 for the initial cup and $ 1.50 for each additional cup.
C(x) = $ 2.95 + $ 1.50 * x
We also know that she chose to purchase a bagel for $2.75 and that she received a $0.50 discount.
By adding these we get
C(x) = $ 2.95 + $ 1.50 * x + $ 2.75 = $ 0.50
C(x) = $5.20 + $ 1.50 * x
Now we want to find that she had 2 refills , then the total cost is
C(2) = $ 5.20 + $ 1.50 * 2
= $ 8.20
Therefore, the total cost she spend at the coffee shop = $ 8.20
To learn more about linear equation check the given link
brainly.com/question/4074386
#SPJ1
Name three equivalent fractions to ⅔
Answer:
4/6, 6/9, 8/12, 10/15
Step-by-step explanation:
Find the value of x and snow work please .
Applying angle relationships, the value of x in each figure is determined as:
E. x = 8
F. x = 26
I. x = 9
J. x = 4
How to Apply Angle Relationship to Find the Value of x?Using angle relationship based on the angles involved, create an equation in each case, to enable you find the value of x.
E. 27 + 8x - 1 = 90 [the angle relationship is that they are complimentary angles].
Solve for the value of x:
26 + 8x = 90
8x = 90 - 26
8x = 64
x = 8
F. 7x - 44 = 75 + 63 [vertical angles are congruent]
7x = 182
7x/7 = 182/7
x = 26
I. 180 - (5x - 3 + 13x + 4) = 17 [vertical angles are congruent]
180 - (18x + 1) = 17
180 - 18x - 1 = 17
179 - 18x = 17
-18x = 17 - 179
-18x = -162
x = 9
J. 3y + 10 = 5y - 24 [vertical angles are congruent]
Solve for y
3y - 5y = -10 - 24
-2y = -34
y = 17
Find the value of x:
3y + 10 + 9x + 1 + 82 = 180 [angles on a straight line equals 180 degrees]
3y + 9x + 93 = 180
Plug in the value of y
3(17) + 9x + 93 = 180
51 + 9x + 93 = 180
9x + 144 = 180
9x = 180 - 144
9x = 36
x = 4
Learn more about angle relationships on:
https://brainly.com/question/12591450
#SPJ1
it cost ayden $1.26 to send 9 text messages. how much does each text cost to send
number of texts x price per text = total price
9 x price per text = 1.26
price per text = 1.26/9
price per text = $0.14
Hope this helps :)
-Jeron
If you need any more help on this just comment
Please help! Provide an answer with an explanation to my question & you will receive a 100 points for one question! :)
Answer:
B
Step-by-step explanation:
Standard deviation is the average distance away from the mean, thus B is correct
How many different flag can be made from 10 colors of cloth if each flag is consist of 3 diffferent stripes?
Answer: 1000 different flags
Step-by-step explanation:
So for the flag there are 10 color options and you need to have 3 different stripes. Where you are able to use a color more than once.
For the first stripe there are 10 options so it can be any of the 10 choices.
For the second option you are able to use any of the 10 colors again so it can be any of the 10 colors.
For the last option for stripe 3 you can pick from ay of the 10 colors so there are 10 color options is could be.
Now that you know the how many choices of color there can be for each stripe you multiple the color choice for each stripe by each other to get the number of combinations for different flags.
colors for stripe 1x colors for stripe 2x colors for stripe 3= # of different flags
10x10x10=1000
so there can be 1000 different 3 stripe flags that can be made with 10 colors
Allen is showing his work in simplifying -8.3 + 9.2 - 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning. Write feedback to Allen explaining the mistake he made and how to correct his work.
Step Work Reasoning
−8.3 + 9.2 − 4.4 + 3.7 Original problem
1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse
2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property
3 −8.3 + (4.4 + 9.2 + 3.7) Associative property
4 −8.3 + 17.3 Simplify
5 9 Simplify
The value of the expression -8.3 + 9.2 - 4.4 + 3.7 is 0.2.
What is Number system?A number system is defined as a system of writing to express numbers.
Allen is showing his work in simplifying -8.3 + 9.2 - 4.4 + 3.7.
The given expression is -8.3 + 9.2 - 4.4 + 3.7.
The additive inverse should be as below
8.3-9.2+4.4-3.7
It is the error of Allens work.
-8.3 + 9.2 - 4.4 + 3.7.
-8.3-4.4+9.2+3.7
-12.7+12.9
Apply commutative property
12.9-12.7
0.2
Hence, 0.2 is the value of the expression -8.3 + 9.2 - 4.4 + 3.7.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ1
You have some property that has an assessed value of $74,000. If the tax rate is $7.79 per $100 of assessed value, calculate the tax due.
Find percent tax.
7.79/100 * 100
7.79 percent.
Take 7.79 percent of 74,000.
0.0779 * 74,000 = 5764.6
Sally has 2 cats and each cat eats of a tin of cat food each day.
Sally buys 7 tins of cat food.
For how many days will the cat food feed her 2 cats?
You must show your working.
days=?
Answer:
Step-by-step explanation:
9 tins of cat food feed her 2 cats for 18 days
Step-by-step explanation:
Sally has 2 cats
food eaten by 1 cat each day =
food eaten by 2 cat each day= tins
sally buys 9 tins of cat food
then
tins required in = 1 day
1 tin required in
i.e 1 tin required in 2 days
9 tin required for = 9×2 = 18 days
hence , 9 tins of cat food feed her 2 cats for 18 days
#Learn more :
Sue has 2 cats. Each cat eats 1/4 tin of food each day. Sue buys 8 tine of cat food. Has sue got enough cat food to feed her 2 cats for 14 days?
I need help with this. Reasons are below :)
Answer:
2.) definition of vertical angles
3.) the vertical angles theorem
4.) symmetric property of congruence
Factor 2/3x+4 2/3 linear equation hint 2/3 is gcf please help!!!!!
Answer:
To factor the expression 2/3x + 4, we first need to find the greatest common factor (GCF) of the coefficients of the terms in the expression. In this case, the GCF is 2/3, so we can write the expression as (2/3)(x + 12/2). This is the factored form of the expression, and it can be simplified to (1/3)(2x + 6).
Step-by-step explanation:
find the surface area of the composite figure 5, 5, 3, 4, 3, 4, 5, 2
The surface area of the composite figure is 186 cm².
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Composite figure.
Two boxes.
The surface area of a box.
= 2 x (length x width + length x height + width x height)
Now,
The box on the bottom.
length = 5 cm
Width = 5 cm
Height = 3 cm
Surface area = 2 x (25 + 15 + 15) = 2 x 55 = 110 cm²
The box on the top.
length = 2 cm
Width = 5 cm
Height = 4 cm
Surface area = 2 x (10 + 8 + 20) = 2 x 38 = 76 cm²
Now,
The surface area.
= 110 + 76
= 186 cm²
Thus,
The given composite figure surface area is 186 cm².
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Read the following statement: All real numbers have a reciprocal. Which of the following choices is a counterexample to the statement?
0
1
-7
1/4
Reciprocal of zero is undefined. So all the real numbers do not have the
reciprocal.
What is a reciprocal?The definition of reciprocal in mathematics is the inverse of a value or a number. If n is a real number, then 1/n will be n's reciprocal.
We have the statement,
''All real numbers have a reciprocal''.
To find a counterexample:
The reciprocal of the number zero will always have the value "undefined".
Since there is no number that, when multiplied by zero, produces the result 1.
If n is a real number, then 1/n will be n's reciprocal.
n = 1,
So, the reciprocal of 1 is 1/1 = 1.
n = -7,
So, the reciprocal of -7 is 1/-7= -1/7.
And n = 1/4
So, the reciprocal of 1/4 is 1/(1/4)= 4/1 = 4.
Hence, reciprocal of zero gives us to disprove the statement.
Therefore, All real numbers have the reciprocal, except zero.
To learn more about the reciprocal;
https://brainly.com/question/15590281
#SPJ1
Max draws 2 rectangles each with an area of 24 square centimeters what could be the side lengths of max rectangles
Answer:
see explanation
Step-by-step explanation:
1 rectangle could have the side lengths of 6 and 4
The other could have the side lengths of 8 and 3
(Hope this is what the question asked)
a train leaved the station at 5=0 traveling at a constasnt speed the train travels 360 kilometer in 3 hours Write a function that relates the distance traveled d to the time t
The function is determined using speed and is found to be d = 120t.
What is speed?Speed is generally the change in distance per unit time. (rate of change of distance)
What is the formula of speed?To calculate speed, we will use speed = distance/time.
speed = 360/3
= 120km/hr
Since, the train is moving with a constant speed the ratio of distance and time will be equal to 120 throughout the journey.
120 = d/t
Hence, d = 120t.
To learn more about speed visit the link below:
brainly.com/question/28224010
#SBJ4